For quantum gravity, we will consider the universality class of quantum Einstein gravity (QEG) meaning that it is associated to the quantisation of the physical degrees of freedom associated to Einstein's theory of gravity. As such, in this paper by the Gaussian fixed point (GFP) in the context of gravity we refer to the one associated to the linearised Einstein–Hilbert action unless otherwise stated. Here we should point out that we mean something more specific (but perhaps more deserving of the name) by QEG than the more broad definition given, e.g., in [1]}. In particular, we do not only specify the fields and symmetries, in terms of which we parameterise the theory, but also the physical degrees of freedom. For example, a quantisation of higher derivative gravity [2]} can be carried out by quantising the metric assuming diffeomorphism invariance, but it is a quantisation of more degrees of freedom than Einstein's theory. This shift of emphasis to the physical degrees of freedom and the physical essential couplings will bring our investigation of asymptotic safety closer to the original formulation [3]} by S. Weinberg: a move which has been strongly encouraged recently [4]}.
